Determine angle between 2 vectors.

Question

If there are two vectors given $$\vec {OA} = \hat i + 2\hat j~~\text{and}~~\vec {OB} = 4\hat i + p\hat k $$

Then find the values of $p$ for which $\angle AOB = \cos^{-1}(\frac{1}{5})$.

Would someone please give me a hand on solving this?

Answer 1

HINT:

Try to use Dot product rule.which is $$\vec A. \vec B=|\vec A|.|\vec B|.cos \theta $$ Here, $$\vec A= \hat i + 2\hat j,\vec B=4\hat i + p\hat k$$ $$|\vec A|=\sqrt{1^2+2^2}=\sqrt{5}~~,~~|\vec B|=\sqrt{16+p^2}$$ $$\theta=\cos^{-1}(\frac{1}{5})$$

If you substitute everything in the formula I think you will get, $$p=\pm 8$$